### Abstract

In this paper, we prove that the dimension of the space spanned by the characters of the symmetric powers of the standard n-dimensional representation of S_{n} is asymptotic to n^{2}/2. This is proved by using generating functions to obtain formulas for upper and lower bounds, both asymptotic to n^{2}/2, for this dimension. In particular, for n ≥ 7, these characters do not span the full space of class functions on S_{n}.

Original language | English (US) |
---|---|

Pages (from-to) | 1-8 |

Number of pages | 8 |

Journal | Electronic Journal of Combinatorics |

Volume | 7 |

Issue number | 1 R |

State | Published - 2000 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

### Cite this

_{n}.

*Electronic Journal of Combinatorics*,

*7*(1 R), 1-8.

**A note on the symmetric powers of the standard representation of S _{n}.** / Savitt, David L; Stanley, Richard P.

Research output: Contribution to journal › Article

_{n}',

*Electronic Journal of Combinatorics*, vol. 7, no. 1 R, pp. 1-8.

_{n}. Electronic Journal of Combinatorics. 2000;7(1 R):1-8.

}

TY - JOUR

T1 - A note on the symmetric powers of the standard representation of S n

AU - Savitt, David L

AU - Stanley, Richard P.

PY - 2000

Y1 - 2000

N2 - In this paper, we prove that the dimension of the space spanned by the characters of the symmetric powers of the standard n-dimensional representation of Sn is asymptotic to n2/2. This is proved by using generating functions to obtain formulas for upper and lower bounds, both asymptotic to n2/2, for this dimension. In particular, for n ≥ 7, these characters do not span the full space of class functions on Sn.

AB - In this paper, we prove that the dimension of the space spanned by the characters of the symmetric powers of the standard n-dimensional representation of Sn is asymptotic to n2/2. This is proved by using generating functions to obtain formulas for upper and lower bounds, both asymptotic to n2/2, for this dimension. In particular, for n ≥ 7, these characters do not span the full space of class functions on Sn.

UR - http://www.scopus.com/inward/record.url?scp=4043106163&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4043106163&partnerID=8YFLogxK

M3 - Article

VL - 7

SP - 1

EP - 8

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

SN - 1077-8926

IS - 1 R

ER -